Relativistic low-momentum interactions from renormalization group

The relativistic $V_{\mathrm{low}k}$ is developed from a renormalization group method for the first time, to provide softened NN interactions for relativistic $abinitio$ calculations. Starting from a given bare NN interaction, the renormalization group method eliminates the repulsive core while keeping the low-energy on-shell T-matrix and, consequently, the two-body observables unchanged. We derive the relativistic $V_{\mathrm{low}k}$ interactions from the relativistic Bonn NN interactions across a wide range of cutoffs and study nuclear matter using the relativistic Brueckner-Hartree-Fock theory in the full Dirac space. Our results demonstrate that the resulting relativistic $V_{\mathrm{low}k}$ interactions provide a proper description of nuclear saturation, exhibiting only mild cutoff dependence. Therefore, the relativistic $V_{\mathrm{low}k}$ shows promise for providing reliable softened NN interactions for future relativistic $abinitio$ calculations of finite nuclei.